If f (x) is a linear function and the domain of f (x) is the set of all real numbers, which statement cannot be true?

A) The graph of f (x) has zero x-intercepts.

B) The graph of f (x) has exactly one x-intercept.

C) The graph of f (x) has exactly two x-intercepts.

D) The graph of f (x) has infinitely many x-intercepts.

Question

Mathematics

Broderick Washington

3 January, 16:49

If f (x) is a linear function and the domain of f (x) is the set of all real numbers, which statement cannot be true?

A) The graph of f (x) has zero x-intercepts.

B) The graph of f (x) has exactly one x-intercept.

C) The graph of f (x) has exactly two x-intercepts.

D) The graph of f (x) has infinitely many x-intercepts.

+5

Answers (1)

Know the Answer?

Samara Newton · Answer 1

A function is said to be a linear function if the graph of the function is a straight line. The graph of a linear function usually have a y-intercept and an x-intercept. The graph of f (x) can have zero x-intercept when the straigh line is a horizontal line other than the x-axis. The graph of f (x) can have one x-intercept, for non-horizontal lines. The graph of f (x) cannot have exactly two x-intercepts. The graph of f (x) can have infinitely many x-intercepts when the straight line coincides with the x-axis. Therefore, if f (x) is a linear function and the domain of f (x) is the set of all real numbers, the statement that cannot be true is "The graph of f (x) has exactly two x-intercepts."